"Solutions to the RH and and related mathematical research areas

 Disclaimer: with the exception of the last section D all papers of this page are without authorization from the ivory tower


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A. A Kummer function based Zeta function theory

to prove the Riemann Hypothesis




The Riemann Zeta function












B. A new ground state energy model of the harmonic quantum oscillator





The Bose-Einstein condensate




We provide a new ground state energy model which ensures convergent quantum oscillator energy series. This enables the definition of a truly infinitesimal geometry based on a non-ordered, still Archimedian field. The corresponding inner product with its induced norm defines the appropriate metric. The (Hilbert space) domains of related self-adjoint, positive definite operators to build appropriate eigenpair structures are built on Cartan´s differential forms. By this, H. Weyl´s "truly" infinitesimal (affine connexions, parallel displacements, differentiable manifolds based) geometry is replaced by a truly infinitesimal (rotation group based) geometry (corresponding to continuous manifolds, only):




May 2017 summary



A new H(-1/2) Hilbert space based ground state energy model of the harmonic quantum oscillator



 Relationships/opportunities to a related quantum gravity model






Further related/supporting papers


                   Braun K., "An alternative quantization of H=xp"













C. A global unique weak H(-1/2) solution of the Navier-Stokes initial value problem 




earlier published versions





D. PhD thesis




Besides the interior error estimates the paper proves the quasi-optimal approximation behavior of the Ritz-Galerkin method in a Hilbert scale framework. The example 2 gives the model operator of the Symm (Pseudo-Differential) integral operator. Other examples would be the Calderon-Zygmund (singular integral) operator or the Hilbert transform (singular integral) operator.